Eisenberg was for many years a biomedical engineer at Rockefeller University, where he and Dr. Robert Schoenfeld were co-heads of the Electronic Lab.[4] He designed the first transistorized radio frequency coupled pacemaker in about 1960 in collaboration with Dr. Alexander Mauro. It is currently on display at Caspary Hall, Rockefeller University.

Eisenberg published his first short story, "Dr. Beltzov's Polyunsaturated Kasha Oil Diet," in Harper's Magazine in 1962. Shortly after that, he began publishing his stories in many of the leading science fiction magazines of the day, including The Magazine of Fantasy and Science Fiction, Galaxy Science Fiction, and If. Many of these stories have a humorous style and feature his character Professor Emmet Duckworth, a research scientist and two-time winner of the Nobel Prize.

Eisenberg is best known for his short story What Happened to Auguste Clarot?, which was published in the anthology Dangerous Visions edited by Harlan Ellison. His stories have also been reprinted in anthologies such as Great Science Fiction of the 20th Century, The 10th Annual of the Year’s Best SF, and Great Science Fiction By the World's Great Scientists.

He has published two books of limericks (both with George Gordon), and one collection of short stories, Best Laid Schemes. More recently, he has gained a cult following for the limericks he posts in the comments sections of various New York Times articles[5] and has been called the "closest thing this paper has to a poet in residence."[6]

"The Time of His Life," The Magazine of Fantasy and Science Fiction, April 1968. Reprinted in Alpha 1 edited by Robert Silverberg, 1970; Arbor House Treasury of Modern SF edited by Robert Silverberg, Martin H. Greenberg, Arbor House, 1980; Great Science Fiction of the 20th Century edited by Robert Silverberg, Martin H. Greenberg, Avenel Books, 1987.

"A Matter of Time and Place," The Magazine of Fantasy and Science Fiction, January 1970.

"The Cameleon," The Magazine of Fantasy and Science Fiction, March 1970. Reprinted in American Government Through Science Fiction edited by Joseph D. Olander, Martin H. Greenberg, and Patricia S. Warrick, McNally, 1974; Election Day 2084: Science Fiction Stories About the Future of Politics edited by Isaac Asimov and Martin H. Greenberg, Prometheus, 1984;